Digital-Analog Simulations of Schr\"odinger Cat States in the Dicke-Ising Model

TL;DR

This paper proposes a digital-analog quantum simulation method for the Dicke-Ising model, enabling the creation and detection of Schr"odinger cat states associated with superradiant phase transitions, overcoming experimental limitations.

Contribution

It introduces a novel digital-analog quantum algorithm and a parity-measurement protocol to simulate and analyze Schr"odinger cat states in the Dicke-Ising model.

Findings

Successful simulation of superradiant ground states

Generation of photonic Schr"odinger cat states

Wigner tomography for state verification

Abstract

The Dicke-Ising model, one of the few paradigmatic models of matter-light interaction, exhibits a superradiant quantum phase transition above a critical coupling strength. However, in natural optical systems, its experimental validation is hindered by a "no-go theorem''. Here, we propose a digital-analog quantum simulator for this model based on an ensemble of interacting qubits coupled to a single-mode photonic resonator. We analyze the system's free energy landscape using field-theoretical methods and develop a digital-analog quantum algorithm that disentangles qubit and photon degrees of freedom through a parity-measurement protocol. This disentangling enables the emulation of a photonic Schr\"odinger cat state, which is a hallmark of the superradiant ground state in finite-size systems and can be unambiguously probed through the Wigner tomography of the resonator's field.